1. Field of the Invention
Embodiments of the present invention relate to high-performance computing. More particularly, embodiments of the present invention relate to a system for a conjugate gradient iterative linear solver that calculates the solution to a matrix equation.
2. Description of the Related Art
Large systems of linear equations may be expressed in the form of the matrix equation: Ax=b. A is a known matrix of size n×n, where n is usually quite large. b is a known vector of size n. x is an unknown vector of size n, for which a solution is desired. The A-matrix is positive-definite, if it satisfies the condition that for every non-zero vector x: xTAx>0, where xT is the transpose of the x-vector. When the A-matrix is positive-definite, the conjugate gradient method of solving the matrix equation may be applied.
Utilizing software techniques and single processor systems to find the solution to the matrix equation typically results in a plurality of calculations that are performed in a serial fashion. These approaches don't take advantage of the possibility that some of the calculations of the conjugate gradient method may be performed in parallel.